Question

[Nhi Phạm Yến]

so sánh

A=\(\dfrac{10^{1990}+1}{10^{1991}+1}\)

B=\(\dfrac{10^{1991}+1}{10^{1992}+1}\)

nhanh nha mik đang cần gấp (giải thích rõ nha)

Answer 1

[Nguyễn Thanh Hằng]

Ta có :

\(10A=\dfrac{10\left(10^{1990}+1\right)}{10^{1991}+1}=\dfrac{10^{1991}+10}{10^{1991}+1}=\dfrac{10^{1991}+1+9}{10^{1991}+1}=1+\dfrac{9}{10^{1991}+1}\left(1\right)\)

\(10B=\dfrac{10\left(10^{1991}+1\right)}{10^{1992}+1}=\dfrac{10^{1992}+10}{10^{1992}+1}=\dfrac{10^{1992}+1+9}{10^{1992}+1}=1+\dfrac{9}{10^{1992}+1}\left(2\right)\)

Lại có : \(1+\dfrac{9}{10^{1991}+1}>1+\dfrac{9}{10^{1992}+1}\)

\(\Leftrightarrow10A>10B\Leftrightarrow A>B\)

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